There is currently a great interest in the semiconductor industry in the determination of the mechanical stress in thin films. Films that are in a state of high stress can fracture, delaminate from a substrate or film onto which they are deposited, or can cause another film or the substrate to fracture. Any of these occurrences can result in the failure of an integrated circuit chip that includes the film. It is therefore desirable to have a technique for determining an amount of stress in a thin film, preferably by a non-contact and non-destructive method.
The stress that is present in a material is specified through a stress tensor .sigma.. The elements of this tensor are the coefficients .sigma..sub..alpha..beta., where the indices .alpha. and .beta. run from 1 to 3. Thus, for example, .sigma..sub.11 indicates the force per unit area acting in the x-direction on a surface of the material whose plane is normal to the x-direction. At a free surface of a material, i.e., a surface which is not subjected to any external forces, the normal component of the stress must vanish. A uniform planar film deposited onto a substrate whose surface lies in the xy-plane will have a surface normal to the z-direction. Thus, the component .sigma..sub.33 of the stress tensor must vanish at the top surface of the film. For a film in a state of stress the components .sigma..sub.11 and .sigma..sub.22 of the stress tensor may be non-zero. In many situations of interest these two components are equal. In such circumstances it is customary to specify the stress by the in-plane pressure P defined as EQU P=-.sigma..sub.11 =-.sigma..sub.22 ( 1)
In one known method for stress measurement a blanket film is deposited onto a substrate (see, for example, A. K. Sinha, H. J. Levinstein, T. E. Smith, J. Appl. Phys. 4, 2423 (1978)). The stress in the film is then determined from a change in the curvature of the wafer that is produced following the deposition of the film. The curvature is commonly measured either via a differential capacitance technique or by laser deflection. Thus, the radius of curvature R of the wafer is measured together with the thickness d.sub.f of the film and the thickness d.sub.s of the substrate. The stress P is then found from the relation EQU P=(Y.sub.s d.sub.s.sup.2)/6R(1-.nu..sub.s)d.sub.f !, (2)
where Y.sub.s is Young's modulus for the substrate and .nu..sub.s is Poisson's ratio for the substrate. If the substrate takes on a shape which is convex on the side where the film is deposited, this condition indicates that the stress is compressive, i.e. P is positive.
However, the measurement of wafer curvature can only be used to indicate the average stress over a large area of the film. It cannot be used to measure stress within a small region of a film, or to find the stress in a film deposited onto a small area of the substrate.
A second known method to determine the amount of stress in a film is by Raman spectroscopy. By means of a light scattering measurement a change in the photon frequencies is measured. The change in photon frequency is proportional to the stress, and the coefficient of proportionality has been measured for a number of materials. Hence, a measurement of the shift can be used to determine the stress. However, the Raman spectroscopy measurement can only be applied to crystalline materials, is of limited accuracy, and requires a considerable amount of time to perform, all of which limit its application to the measurement of film stress in an integrated circuit processing environment.
A third known method to determine the amount of stress in a film uses X-ray diffraction to measure the stress (see, for example, P. A. Flinn et al., Journal of Applied Physics 67, 2927 (1990)). The scattering of X-rays from the film is detected and the dimension of a unit cell of the film material is determined. By comparison of the measured dimension of the unit cell with the corresponding dimensions of the unit cell in an unstressed bulk sample of the same material, the elastic strain can be determined. From the strain the stress can be calculated using the equations of elasticity. However, this X-ray method has the following limitations: 1) it can only be applied to crystalline materials; 2) it is difficult to apply to determine the stress in very small areas of a film (for example, areas with linear dimensions 10 microns); and 3) the measurement cannot be made in short time. As a consequence, the X-ray technique has limited applicability to the measurement of film stress in an integrated circuit processing environment.
In U.S. Pat. No. 5,546,811, "Optical Measurements of Stress in Thin Film Materials", Rogers et al. disclose an optical method for measuring an effect of residual stress in an unsupported film. In the technique of Rogers et al. optical excitation is used to excite an unsupported region of the film thereby generating surface propagating waveguide or "Lamb" modes in the film. A measurement of time or frequency dependent properties of the film are compared to properties of a second unsupported thin film, having known residual stress properties. In a further embodiment a determined phase velocity is compared to one calculated from a mathematical model using equations of motion for a stressed, unsupported film system.